These observations are the starting point for the content of second part of the paper.
After a brief review of the state sum construction of area-dependent quantum field
theories from regularised Frobenius algebras and their bimodules in
Section REF , we make the
mathematical structure of topological defects in two-dimensional Yang-Mills theories
precise by introducing an idempotent complete bicategory of topological defects
in Section REF .
The input for a generalized orbifold construction in this framework is a strongly
separable symmetric Frobenius algebra in an endomorphism category inside the topological defect
bicategory. In Section REF  we construct such a Frobenius
algebra from
the defects which is isomorphic to a Frobenius algebra built from a bimodule
structure on the square-integrable functions \(L^2(G\rtimes \mathsf {Out}(G))\)  on the semi-direct
product \(G\rtimes \mathsf {Out}(G)\) . In Section REF  we compute the corresponding
orbifold theory using the state sum construction and show, using the abstract
orbifold completion of the defect bicategory [1]}, that the backwards orbifold
can be performed using Wilson line defects in Section REF .
